Perturbation analysis of conjugate MI-ESPRIT for single acoustic vector-sensor-based noncircular signal direction finding
Perturbation analysis of conjugate MI-ESPRIT for single acoustic vector-sensor-based noncircular signal direction finding
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DOI：
10.1016/j.sigpro.2006.12.016
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发表时间：
2007-07
期刊：
影响因子：
--
通讯作者：
Yougen Xu;Zhiwen Liu;Jinliang Cao
中科院分区：
文献类型：
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作者：
Yougen Xu;Zhiwen Liu;Jinliang Cao
本文分析了闭合形式共轭多不变ESPRIT(CMI-ESPRIT)算法：(1)利用非圆信号的非零共轭二阶和四阶累积量的冗余性；(2)识别自由空间中声矢量传感器固有的实值二维指向性。给出了在CMI-ESPRIT中起关键作用的范数惩罚ESPRIT矩阵和子空间约束ESPRIT矩阵的摄动分析。结果表明，范数惩罚的ESPRIT矩阵是有偏的(但有界的)，且对某个有限的正则化因子具有最小均方误差(MSE)；而子空间约束的ESPRIT矩阵是无偏的，当正则化因子为无穷大时，其均方误差趋于最小。这些观测结果对确定正则化参数有潜在的帮助，而正则化参数对CMI-ESPRIT的性能具有重要意义。这些结果也有助于最终研究测向精度。给出了仿真结果，验证了分析的正确性。
The closed-form conjugate multiple-invariance ESPRIT (CMI-ESPRIT) algorithm herein analyzed: (1) makes use of redundancy in the nonvanishing conjugated second- and fourth-order cumulants of noncircular signals; (2) recognizes the real-valued two-dimensional directivity inherently achieved by an acoustic vector-sensor in a free-space. It is provided in this correspondence the perturbation analyses on both the norm-penalized and the subspace-constraint ESPRIT matrices that play the key role in the CMI-ESPRIT. It is shown that the norm-penalized ESPRIT matrix is biased (but bounded) and has a minimal mean-squared-error (MSE) for some finite regularization factor, whereas the subspace-constraint ESPRIT matrix is unbiased and its MSE approaches minimum when the regularization factor becomes infinite. These observations are potentially useful for the determination of the regularization parameters which is significant for the performance of CMI-ESPRIT. The results also contribute to the ultimate study of direction-finding accuracy. Simulation results are presented to validate the given analyses.